The Fundamental Plane Is Not a Plane: Warped Nature of the Fundamental Plane of Early-type Galaxies and Its Implication for Galaxy Formation

Based on $16,283$ early-type galaxies (ETGs) in $0.025\le z_{\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}}<0.055$ from Sloan Digital Sky Survey data, we show that the fundamental plane (FP) of ETGs is not a plane in the strict sense but is a curved surface with a twisted shape whose orthogonal direction to the surface is shifted as the central velocity dispersion (${\sigma }_0$) or mean surface brightness within the half-light radius (${\mu }_e$) changes. When ETGs are divided into subsamples according to ${\sigma }_0$, the coefficient of ${\mu }_e$ of the FP increases, whereas the zero-point of the FP decreases at higher ${\sigma }_0$. Taking the $z$ band as an example, the coefficient of ${\mu }_e$ rises from $0.28$ to $0.36$ as ${\sigma }_0$ increases from $\sim 100$ to $\sim 300$ km s${}^{-1}$. At the same time, the zero-point of the FP falls from $-7.5$ to $-9.0$ in the same ${\sigma }_0$ range. The consistent picture on the curved nature of the FP is also reached by inspecting changes in the FP coefficients for ETG subsamples with different ${\mu }_e$. By examining scaling relations that are projections of the FP, we suggest that the warped nature of the FP may originate from dry merger effects that are imprinted more prominently in ETGs with higher masses.